sin(arctan((-5)/(12)))

解答

sin (arctan (\frac{- 5}{12}))

- \frac{5}{13}

十进制

- 0.38461 \dots

求解步骤

sin (arctan (\frac{- 5}{12}))

使用三角恒等式改写:

sin (arctan (\frac{- 5}{12})) = \frac{( \frac{- 5}{12} ) 1 + ( \frac{- 5}{12} ) ^{2}}{1 + ( \frac{- 5}{12} ) ^{2}}

利用以下特性:

sin (arctan (x)) = \frac{x 1 + x ^{2}}{1 + x ^{2}}

= \frac{( \frac{- 5}{12} ) 1 + ( \frac{- 5}{12} ) ^{2}}{1 + ( \frac{- 5}{12} ) ^{2}}

= \frac{\frac{- 5}{12} 1 + ( \frac{- 5}{12} ) ^{2}}{1 + ( \frac{- 5}{12} ) ^{2}}

化简

= - \frac{5}{13}

2 arctan (2) - arcsin (\frac{3}{5})

4 cos (2 (0))

cos (\frac{25 π}{4})

2 (sin (4) + cos (4) + 4 (cos (4) - sin (4)))

1 - \frac{sin ( 4 5 ^{\circ} )}{cos ( 4 5 ^{\circ} )}